With the evolution from the Code-Division Multiplex Access (CDMA) network to the Long Term Evolution (LTE) network, gradually services will be borne by the LTE network. At the initial stage of LTE network establishment, the main purpose is to cover hot spot areas and provide high-speed non-real-time data services. Voice Over Internet Protocol (VoIP) is not deployed. Voice services were still borne by 1x Circuit Service (CS). Therefore, the inter-working between the CDMA20001 1x and the LTE mainly lies in the support of 1x Circuit Service Fall Back (1xCSFB). FIG. 1 shows network architecture of 1xCSFB according to the relative art. As shown in FIG. 1, one of logic functions of the Inter-working Solution (IWS) is to serve as a CDMA 1x message translation. That is, information or message of 1x network air interface sent by a terminal through an LTE network air interface has to be sent to the IWS first and then forwarded by the IWS to a 1x core network switch. Similarly, if information or message from the switch of the 1x network needs to pass through the LTE network air interface to be sent to the terminal, then the information or message has to be sent to the IWS first and then forwarded by the IWS to the LTE network. The logic functions of the IWS may be realized in a 1x Base Station Controller (1x BSC), may be realized in a Mobile Switching Center (MSC), may be realized in a Mobility Management Entity (MME) in the LTE network, and also may be independent network entities. In order to standardize processing at the terminal side and the network side, CDMA Standards define a general circuit service notification application (GCSNA) protocol to support inter-working among the CDMA2000 1x, the LTE and other radio access technologies. The GCSNA protocol defines formats of 1x messages which can be carried in a General Circuit Service Notification Application 1x Circuit Service (GCSNA1xCircuitService) message. According to regulations of the protocol, it is only allowed to carry one 1x Layer3 message in the GCSNA1xCircuitService message. In this way, processing in some situation will be failed. For example, in order to synchronously send a plurality of 1x Layer3 messages and guarantee the time sequence of processing the messages, under the related mechanism it needs a plurality of GCSNA1xCircuitService messages to respectively carry one 1x Layer3 message. Due to the complexity (such as message loss retransmission and packet cache) of the air interface transmission mechanism, it is unable to guarantee the synchronous sending and receiving of messages, thereby causing the failed inter-working processing between the CDMA2000 1x and other radio access technologies including the LTE.